Apologies for the bluntness, but you sound like you need a reality check.
A friend loved her job at a funeral director's. Did it for years. Described it as 'the best job in the world'.
And then she had what she calls 'a Maggot Incident'.
She's been unable to sleep without strong medication for five years, has gone from a healthy weight to cadaverous, as she cannot eat anything without vomiting and in all likelihood, isn't ever going to work again, despite access to a seemingly bottomless pit of funding from her employer for her to have support, counselling, treatment and full wages for two years. Her employers have done everything they can to help, but what she experienced on one evening has been too much for her to bear.
Another friend hasn't worked for ten years since being a SOCO. He has nightmares, as he describes it, without needing to close his eyes.
The man who ran the local hospital mortuary perfectly happily for ten years committed suicide in the sluice room - the belief is that there wasn't a particular event that triggered this, but it was an accumulation of his day to day work that affected him. The first job for the replacement was his predecessor. (I think that processes may have changed now, though).
I did a secondment in a mortuary. The humour would be horrific to anybody else (nothing insulting to the deceased but you can't get darker than finding something funny in the mortuary) - but they all have their quiet tales and their 'If this happens, I'm done' points. There were the terrorist incidents, the disasters, the multiple accidents. All of these affect people differently; the sheer numbers, the work, the conditions, being tired but unable/feeling unable to stop until the work is done. It's very, very demanding emotionally and physically.
It's not like on the telly at all. I did the secondment because they desperately needed somebody and I was the only person who didn't shrink away with horror at the thought. I don't regret it in the slightest. But some things will stay with you for a very, very long time - it might be the sight, it might be the sound, it could very well be a smell - it might be a personal connection.
Be very aware that having a cast iron stomach and wanting to help people or being fascinated by a taboo subject is no defence against your own mind as a result of what you witness. And other than colleagues or a specialist professional when it becomes too much, you will have nobody to talk to about it - no 'how was work today?' as you come in and hang your coat up dash upstairs to shower for an hour. What you experience will be yours alone - there will be no unwinding with a mate after work and joking about your job if they don't do similar.
Curiosity is not a useful characteristic. Because you won't be needing it.
You'll see stuff you have never imagined anyway.
Still interested? Get some specific ideas as to direction and start approaching potential employers.